Calculating Overall Efficiency
Using the energy efficiency concept, we can calculate the component and overall efficiency:
Here the electrical energy is given in Wh and Chemical Energy in Btus. So Wh can be converted to Btus knowing that there are 3.412 Wh in a Btu.
This overall efficiency can also be expressed in steps as follows:
Applying this method to the above power plant example:
It can be seen that the overall efficiency of a system is equal to the product of efficiencies of the individual subsystems or processes. What is the implication of this?
Steps of Overall Efficiency
We have been looking at the efficiencies of an automobile or a power plant individually. But when the entire chain of energy transformations is considered—from the moment the coal is brought out to the surface to the moment the electricity turns into its final form—true overall efficiency of the energy utilization will be revealed. The final form at home could be light from a bulb or sound from a stereo. The series of steps as shown in the figure below are: 1) Production of coal (Mining), 2) Transportation to power plant, 3) Electricity generation, 4) Transmission of electricity, and 5) Conversion of electricity into light (Use).
We know what the cumulative efficiency is actually. We looked at that in the previous diagram. We talked about it. On this diagram, we are looking at cumulative or overall efficiency for a qualified power plant. Basically, in the ground, we have coal, right? We have to bring the coal out to the surface. That step is called mining. Obviously, we need to spend some energy to bring the coal from the ground to the surface. So mining by itself has some kind of, let's say, about 95% efficient. Or that step is 95% efficient. In other words, if we have 100 units in the ground, and by the time this energy comes out to the surface, we will be left with only 95 units. Because five units, we will be spending in operating the equipment and in bringing the coal from the ground to the surface. Now, this 95 obviously is not readily available, because we need to take these 95 BTUs to a power plant. So the trucks have to use some energy to take these 95 BTUs all the way up to the power plant. So when it reaches the power plant, these 95 units may turn out to be 90 units. In other words, we will be spending about five units in the transportation. So once we put in 90 units into a power plant, which is roughly about by now 33% efficient or 35% efficient, what this tells us is when we put in 90 units into the power plant, the output from the power plant in the form of electricity is only 30 units. So now, at this point, we have only 30 units left over when we started our business with 100 units. Now, these 30 units are transported through these high voltage lines to a user. By the time you get to the user, we're talking about a unit or two lost. All right? And now, when we have about, let's say for simplicity purposes we will still have about 29 units or 30 units. And as you all know, the efficiency of a light bulb is notoriously low. It's about 5% efficient. Which means that out of these 29 units or 30 units that we will get into the home, only 5% of that, or 1.5 units are converted, really, to the light. So we started off with 100, and we ended up with 1.5 units of light. So that means the overall efficiency is 1.5 divided by 100. Both are BTUs here. So the overall efficiency is only 1.5%. That is pathetically low. Which means to use 1.5 units of light, we are taking from Mother Earth 100 units. And along the way, we are dumping about 98.5 units of energy during various steps of conversion processes, and we're using 1.5 BTUs and 1.5%. That is the message.
Efficiency of a Light Bulb
If the efficiency of each step is known, we can calculate the overall efficiency of production of light from coal in the ground. The table below illustrates the calculation of overall efficiency of a light bulb.
Calculation of Overall Efficiency of a Light Bulb
||Cumulative Efficiency or Overall Efficiency
|Extraction of Coal
||94% = (0.96 x 0.98) * 100
||33% = (0.94 x 0.35) * 100
|Transmission of Electricity
||31% = (0.33 x 0.95) * 100
||1.6 % = (0.31 x 0.05) * 100
||18 % = (0.31 x 0.60) * 100
Efficiency of an Automobile
A similar analysis on automobile efficiency is shown in the Figure below.
Overall Automobile Efficiency
The table below shows that only about 10% of the energy in the crude oil in the ground is in fact turned into mechanical energy moving people.
||Cumulative Efficiency or Overall Efficiency
|Extraction of Crude